Method and system for simulating a hydrocarbon-bearing formation

Abstract

The invention is a method for simulating one or more characteristics of a multi-component, hydrocarbon-bearing formation into which a displacement fluid having at least one component is injected to displace formation hydrocarbons. The first step of the method is to equate at least part of the formation to a multiplicity of gridcells. Each gridcell is then divided into two regions, a first region representing a portion of each gridcell swept by the displacement fluid and a second region representing a portion of each gridcell essentially unswept by the displacement fluid. The distribution of components in each region is assumed to be essentially uniform. A model is constructed that is representative of fluid properties within each region, fluid flow between gridcells using principles of percolation theory, and component transport between the regions. The model is then used in a simulator to simulate one or more characteristics of the formation.

1. A computer-implemented method for simulating one or more characteristics of a multi-component, hydrocarbon-bearing formation wherein a displacement fluid comprising at least one component is injected into the formation through at least one well to displace hydrocarbons in the formation, comprising the steps of:
 (a) equating the formation in at least one dimension to a multiplicity of gridcells; 
 (b) dividing at least some of the gridcells into two regions, a first region representing a portion of each gridcell swept by the displacement fluid and a second region representing a portion of each gridcell essentially unswept by the injected fluid, the distribution of components in each region being essentially uniform; 
 (c) constructing a model representative of fluid properties within each region, fluid flow between gridcells using principles of percolation theory to provide fine-grid adverse mobility displacement behavior through functional dependencies, and principles of component mass transfer rate between regions; and 
 (d) using the model to simulate one or more characteristics of the formation. 
 
   
   
     2. The method of  claim 1  wherein step (d) predicts a property of the formation and fluids contained therein as a function of time. 
   
   
     3. The method of  claim 1  wherein the displacement fluid is miscible with hydrocarbons in the formation. 
   
   
     4. The method of  claim 1  wherein the displacement fluid is multiple-contact miscible with hydrocarbons present in the formation. 
   
   
     5. The method of  claim 1  wherein the displacement fluid is carbon dioxide. 
   
   
     6. The method of  claim 1  wherein the displacement fluid comprises hydrocarbon gas. 
   
   
     7. The method of  claim 1  wherein model constructed in step (c) is further representative of energy transport between gridcell regions. 
   
   
     8. The method of  claim 1  wherein the displacement fluid is steam and the model of step (c) is further representative of energy transport between gridcell regions. 
   
   
     9. The method of  claim 1  wherein the gridcells comprises unstructured gridcells. 
   
   
     10. The method of  claim 1  wherein the gridcells are three-dimensional. 
   
   
     11. The method of  claim 1  wherein the gridcells are two-dimensional. 
   
   
     12. The method of  claim 1  wherein the rate of mass transfer of each component is proportional to composition differences and capillary pressure differences between the two regions, and mass transfer mechanisms comprise molecular diffusion, convective dispersion and capillary dispersion. 
   
   
     13. The method of  claim 1  wherein the component mass transfer rate between regions is proportional to driving force times resistance. 
   
   
     14. A computer-implemented method for simulating one or more characteristics of a multi-component, hydrocarbon-bearing formation into which a displacement fluid is injected to displace formation hydrocarbons present in the formation, comprising
 (a) equating at least part of the formation to a multiplicity of gridcells; 
 (b) dividing each gridcell into two regions, a first region representing a solvent-swept portion of each gridcell and a second region representing a portion of each gridcell essentially unswept by the displacement fluid, the fluid composition within each region being essentially uniform; 
 (c) constructing a model comprising functions representative of mobility of each phase in each region using principles of percolation theory to provide fine-grid adverse mobility displacement behavior through functional dependencies, functions representative of phase behavior within each region, and functions representative of rate of mass transfer of each component between the regions; and 
 (d) using the model in a simulator to simulate production of the formation and to determine one or more characteristics thereof. 
 
   
   
     15. The method of  claim 14  wherein steps (a) through (d) are repeated for a plurality of time intervals and using the results to predict a property of the hydrocarbon-bearing formation and fluids contained therein as a function of time. 
   
   
     16. A computer-implemented system for determining one or more characteristics of a multi-component, hydrocarbon-bearing formation into which a displacement fluid having at least one component is injected to displace formation hydrocarbons, said system using a multiplicity of gridcells being representative of the formation, comprising
 (a) a model having each gridcell divided into two regions, a first region representing a portion of each gridcell swept by the displacement fluid and a second region representing a portion of each gridcell essentially unswept by the displacement fluid, distribution of components in each region being essentially uniform and mobility of fluids in each region being determined based on principles of percolation theory to provide fine-grid adverse displacement behavior through functional dependencies; and 
 (b) a simulator, coupled to said model, to simulate the formation to determine one or more characteristics therefrom. 
 
   
   
     17. The system of  claim 16  wherein the model is representative of fluid properties within each region, fluid flow between gridcells, and component mass transfer rate between regions. 
   
   
     18. A method of simulating at least one component of a multicomponent fluid system in a hydrocarbon-bearing formation, whose characterizing features are described by a set of equations, by means of a simulator on a computer, the method comprising the steps of:
 (a) providing a model having each gridcell divided into two regions, a first region representing a portion of each gridcell swept by a displacement fluid and a second region representing a portion of each gridcell essentially unswept by the displacement fluid, distribution of components in each region being essentially uniform and mobility of fluids in each region being determined based on principles of percolation theory to provide fine-grid adverse mobility displacement behavior through functional dependencies; and 
 (b) using in the simulator the model thereby simulating changes of a component in the formation.